KarL05/Aiyiyi's Blog
Inequality Revision 2

Inequalitys with one variable

Log

\[\frac{x}{1+x} \leq \ln(1+x) \leq x \]

\[\frac{1}{1+x} < \ln(1+\frac{1}{x}) < \frac{1}{x} \]

Bernoulli

when n>1

\[ (1+x)^n \geq 1+nx\]

when n<1

\[(1+x)^n \leq 1+nx\]